Preheat your oven to 350 degrees F. Line a 9x13 inch baking pan with parchment paper, leaving a couple of inches of overhang on the long sides so you can lift the bars out easily after baking. Lightly grease the parchment.

Make the oat crust. In a large bowl, stir together the rolled oats, 1 cup flour, 3/4 cup brown sugar, salt, and 1/2 teaspoon cinnamon. Pour the melted butter over the top and stir until everything is evenly moistened and clumping together. Press the mixture firmly and evenly into the bottom of the prepared pan. Use the flat bottom of a measuring cup to pack it down into a compact, even layer.

Bake the crust alone for 12 minutes, until it smells nutty and the edges are just starting to set. Remove from the oven and let it cool for 5 minutes while you make the fillings.

Make the cream cheese layer. Beat the softened cream cheese, granulated sugar, 1 egg, and vanilla extract together with a hand mixer until completely smooth and lump-free, about 2 minutes. Set aside.

Make the pumpkin layer. In a medium bowl, whisk together the pumpkin puree, 1/4 cup brown sugar, 1 egg, cinnamon, ginger, nutmeg, and 1 tablespoon flour until smooth.

Drop spoonfuls of the cream cheese mixture and the pumpkin mixture alternately over the warm crust, covering it as evenly as possible. You do not need to be perfectly precise here. Once all of both fillings are dropped onto the crust, use a toothpick or the tip of a knife to gently swirl them together in a figure-8 pattern. Pull it just enough to create a pretty swirl without fully mixing the two layers together.

Bake for 22 to 28 minutes, until the center looks set and does not jiggle when you gently shake the pan. The edges will be slightly puffed and the top will look dry and matte rather than shiny and wet. Do not overbake or the bars will dry out.

Let the bars cool completely in the pan at room temperature, at least 45 minutes, then refrigerate for a minimum of 1 hour before slicing. This resting time is important. If you cut them warm, the filling will smear and the layers will not hold their shape. Use the parchment handles to lift the whole slab out of the pan, then cut into 16 squares with a sharp knife, wiping the blade between cuts.